In the second episode it went through a wormhole, which allowed it to leave the solar system and then travel faster. I don't think they ever say how fast the moon is moving, but it only spends a few days/weeks in any given solar system as it moves along. Don't look too closely at this part of the show - the moon moved at the speed of plot.

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Also for this particular example the modular cutter is both a component AND a container. When attached it can be an integral part of the modular cutter. I say 'can' because of the wide range of modules available. I cannot stress enough how very detailed and well thought out the Modular cutter module published for GURPS is. It provides a very detailed breakdown on various modules and modular cutter operations.
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The GURPS Traveller Modular Cutter book takes pretty much everything previously published, back to classic, and combines it into one really well designed book. GURPS Traveller in general has what I consider to be the best ship design system in any Traveller edition. (The combat system is painfully detailed though, but has the good points of a single damage scale and mostly avoiding absurd results.)

I generally use GURPS Traveller for ship design, because it mostly gets things right. (I'm not sure whether I like its streamlining rules though.) For character creation, Mongoose wins. For actual play, I'm a rules light guy; PDQ# looks good, for example.

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Modules by definition aren't integral to the ship, hence they can be swapped out without impairing the ship's function.

If you're going by an in-game rules jargon definition, this may be true. (I'm not sure. The rules seem ambiguous in their use of jargon.) But by the common language definition, that's not true. Consider the example of a typical desktop computer. That's very modular. Modules include the case, power supply, motherboard, CPU, CPU cooling system (heat sink or something more elaborate), memory, video adapter, net adapter, audio device, disk drive, solid state drive, optical drive, and external modules such as the screen, speakers, keyboard, mouse, backup power, etc. Some of those are optional, and some are necessary. But they're all module and the system is definitely modular by the normal definition.

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That function is covered by either an External cargo mount if operating solely in space or by the breakaway hull option if you need to operate in atmosphere.

Those are specific in-game mechanisms that allow ships to modular in certain ways. The rules may not define a mechanism, but it should be possible to build a ship that's as modular as a desktop computer -- or as monolithic as a smartphone.

At the referee's discretion very large ships can
be built in a modular fashion allowing simultaneous
construction. This will mean the total construction time
can be reduced by up to 90%. This is typically done
only on ships exceeding 50,000 tons.

The second is spelled out explicitly in its limitations.

This tonnage may not include
the bridge, power plant, drives or any structure or
armour options.

The computer example has the first definition for most of it components, whereas the second definition would only fit the external devices such as usb devices that extend functions but aren't core to the design.

Ships have built in modular format since at least WW1. The Germans built smaller uboats in pieces and shipped them to Turkey via rail to be deployed and assembled in the Black sea.

And the US built liberty ships that way, as well as they build Nimitz class carriers this way.

HOWEVER, while the record for ASSEMBLING a liberty cargo ship is 12 days, this is NOT what you can expect normally. First off none of this takes into account the massive subsidiary set of shops and personnel required to assemble modules, let alone cost or time. Secondly, and more importantly, these timeliness assume a regular production to keep the lines in operation. That's not realistic unless a shipyard is constantly building ships of a specific type every day.

It also calls into consideration some of the underlying factors with modules. They have to be built and assembled pretty specifically to ensure structural integrity. And, as far as I could tell, none of the ships built in modules,either in the beginning or today, carry any sort of armor on them aside from their hulls and a few internal reinforcements. Capital ships were always constructed from the keel up if they were armored. Which makes a lot of sense if you research how armor and structure must be engineered and built together to work properly. Having a 'seam' in your armor or structure would be very bad. While some bracing could be applied, it still wouldn't be as good as if the hull was built with it from the keel up. Or at least not from what I've read. Only a naval architect who knew how to design armored hulls would really be able to answer that. While today's weapons are missiles instead of shells, the idea remains the same - keeping the big boom on the outside.

The rule is ok as it stands, and since MGT prefers expansive rules to specific it should stand as is. It's not a critical rule for gameplay.

Its called mass parallelization as each component is far smaller than the overall project and generally faster on overall construction time.

Hence why this production type is used on most large scale projects.

I understand the principle. But rarely, if ever, is the underlying support structure called out that allows this. All those parallel production lines still need space, people, power, etc. And their build times aren't factored into the final build time (as are none of the other underlying support requirements). But all anybody see's is the end result. Kind of like a million monkeys whacking on typewriters to write a novel. Nobody sees the 999,999 thousand horrible copies, they just see the one good one.

And large scale projects that use modules still have limitations. The example of the liberty ship worked because they were building the same exact ship over and over and over in the yards. But if they needed a ship that was, for example, 40 feet longer, the model would have broken because it can't take any changes but the most simplistic and very, very basic. For Traveller the yards crap out tons of Free Traders - as long as you want a Free Trader exactly like the deck plans call for.

I went on a cruise earlier this month on the Disney Magic. The fore and aft sections of the ship were built in two separate shipyards, and one part was towed to the other and the two sections joined together. I don't know how they did it; surely half a cruise ship isn't easily made seaworthy. But they did it.

My guess is that regular staterooms are built on an assembly line, but the assembly line has to be at least somewhat flexible, because of variations in things like the location of lifeboat mechanisms, whatever structures tied the fore and aft sections together, major infrastructure features, and the curvature of the hull.

The cabin we had was probably mostly custom built, but it was the second largest room type (after the twin Walt Disney and Roy Disney suites), and absurdly large and luxurious. (We spent way too much on it, but it was a gift for my parents' 80th birthdays, and one-time extravagance.) I could see slight imperfections in the woodworking that distinguish hand-built carpentry from assembly line CNC consistency. I studied the construction with thoughts of Traveller lines.

Anyway, my point is that construction can be done with a certain degree of modular production. Game rules don't model it all that well. If using the rules in a context like a Trillion Credit Squadron campaign war game, I'd stick to the rules. But in a context like super-rich player characters ordering a super-yacht or mercenary capital ship, I'd use game master judgment guided by real world construction knowledge.

This video (https://www.youtube.com/watch?v=OzopvJ5vXp4) talks about the two follow-on ships. It not as technical as the others, relatively speaking, but it mentions that the Magic was built in sections because the first yard couldn't accommodate it. Which seems rather odd since they are put together in the yard. Since it was in '97, I'm wondering if they needed to build in two different yards for speed sake. No mention was made about the construction of the last 2.

There are some interesting views of the cabins and such. Lots of ideas if you want to build luxury cabins on a starship. With, perhaps, the exception of the waterslide on top. Though wouldn't it be kind of cool to set that in space and as you jet through the tubes you look above you and see the stars?

That Disney video is interesting, but I'm somewhat amused that Discovery Channel was that receptive to Disney corporate propaganda. But I think Discovery Channel may be owned by Disney , and in that case it makes sense.

It certainly has some good inspiration for luxury starship design. Imagine the wild water slide one could build with Traveller gravity manipulation. Adjust the force to assure safe separation between riders. Rotate the field through a straightaway. Turn it down to almost zero around a turn. Reverse it near the end to slow the rider almost to a stop, then switch it back to deck normal for unloading.

Another inspiration for a luxury starship that might be useful is the GURPS pleasure world booklet. That has not just a lot about the specific world, but adventure seeds for the pleasure world that could, in many cases, be carried aboard a luxury starship.

My idea of the modular cutter was something like Thunderbird 2. This style would take into account the increased hull cost (to account for the module lifting and dropping equipment). It also has a large hole when no module is attached. Some cutter designs I have seen had the strut connecting the flight deck and engineering contain a crawlspace so that both sections could be accessed if needed.
To allow construction of this presumably you really need to drop the requirements in the breakaway ship for a bridge etc. This type of module can have its own power plant etc. Technically it would need this for weapons, life support etc. if deployed away from its cutter.
Just my thoughts though.